Rep. Franks resigned on Dec. 8, 2017, over sexual harassment accusations.
Governor Doug Ducey (R-AZ) will set the date for a special election.
(AZ law requires a special election because Rep. Franks resigned more than 6 months before the next scheduled election in Nov. 2018)

Rep. Becerra resigned after being appointed as California Attorney General to succeed Senator-elect Kamala Harris. Becerra called the appointment by Gov. Jerry Brown a "phenomenal opportunity" but it leaves his constituents unrepresented for months and then burdened by the expense of a Special Election (April 4 with a June 6 runoff).
On April 4, Robert Lee Ahn was defeated in special Democratic primary election. On June 6, Jimmy Gomez defeated William Rodriguez Morrison (R).

Rep. Conyers resigned on Dec. 5, 2017, over sexual harassment accusations.
Governor Rick Snyder (R-MI) opted to keep the House seat vacant for 11 months, until Nov. 2018.
(MI law allows for a special election anytime between now and the next election; Snyder chose the special election date to coincide with the general election date in Nov. 2018)

Rep. Tiberi resigned on Oct. 19, 2017, effective Jan. 31, 2018, to take a job with the Ohio Business Roundtable, leaving his constituents unrepresented, and then requiring taxpayers to foot the bill for a special election to replace him.
Governor John Kasich (R-OH) will set the special election date after Tiberi's resignation takes effect.
Contenders include Democratic Franklin County Sheriff Zach Scott and Republican State Sen. Troy Balderson

Rep. Chaffetz resigned effective June 30, 2017, saying he never intended "a lifetime career" in Congress, choosing instead a job at Fox News, only a few months into a 2-year term. His resignation leaves his constituents unrepresented for months and then burdened by the expense of a Special Election (to be scheduled by Gov. Gary Herbert).